Crossbenchers to rule roost in parliament

Independents will put the 'cross' back into 'cross bench' when they take up a series of issues, from asylum seekers to fighting corruption, in federal parliament next week.

An emboldened group of crossbenchers will seek to put pressure on the government over a national anti-corruption watchdog, a ban on Commonwealth support for coal-fired power stations, urgently transferring ill asylum seekers in offshore detention to Australia and a royal commission into the supermarket and petrol retailing sectors.

Their confidence stems from now holding the balance of power in both the Senate and House of Representatives.

Labor also plans to draw on crossbench concerns by bringing on a bill on Monday to protect gay students from discrimination in faith-based schools.

The government, which supports the principle of the change, says the opposition has not negotiated on the amendment in good faith.

Prime Minister Scott Morrison will be seeking to put parliament's focus to the coalition's preferred battlegrounds of the economy and national security, on his return from the G20 summit in Argentina.

The government is keen for a committee inquiring into its laws to help police and intelligence officers access encrypted communications to report, allowing the bill to pass before Christmas.

The controversy over how almost $450 million was provided to the Great Barrier Reef Foundation will be explored in a report to be tabled during the week.

Independent MP Kerryn Phelps said she hoped to see progress on a number of issues which should be "above politics", such as treating asylum seekers in offshore detention with dignity and respect.

One unresolved issue is whether Home Affairs Minister Peter Dutton, who was away from parliament this week, will be referred to the High Court over eligibility issues.

Mr Dutton has legal advice that his family's child care interests don't breach the constitutional bar on receiving a pecuniary interest from the Commonwealth.

While Labor has been seeking crossbench support, there is a feeling among many of the independents no individual MP should be singled out and instead there should be a "job lot" of referrals covering MPs under a cloud from both major parties.

Once it rises next Thursday, the parliament won't return until February 12.